Surge impedance of microstrip line from frequency

The frequency-dependent surge impedance of a microstrip line can be calculated from its frequency-independent surge impedance and effective permittivity.

surge_impedance

surge_impedance of the microstrip line when frequency dependence is taken into account.

Symbol:

Z_S

Latex:

\(Z_\text{S}\)

Dimension:

impedance

independent_surge_impedance

surge_impedance of the microstrip line when frequency dependence is omitted.

Symbol:

Z_S0

Latex:

\(Z_{\text{S}, 0}\)

Dimension:

impedance

effective_permittivity

relative_permittivity of the microstrip line when frequency dependence is taken into account. See Effective permittivity of microstrip line.

Symbol:

epsilon_eff

Latex:

\(\varepsilon_\text{eff}\)

Dimension:

dimensionless

independent_effective_permittivity

relative_permittivity of the microstrip line when frequency dependence is omitted. See Effective permittivity of microstrip line.

Symbol:

epsilon_eff0

Latex:

\(\varepsilon_{\text{eff}, 0}\)

Dimension:

dimensionless

law

Z_S = Z_S0 * sqrt(epsilon_eff0 / epsilon_eff) * (epsilon_eff - 1) / (epsilon_eff0 - 1)

Latex:
\[Z_\text{S} = Z_{\text{S}, 0} \sqrt{\frac{\varepsilon_{\text{eff}, 0}}{\varepsilon_\text{eff}}} \frac{\varepsilon_\text{eff} - 1}{\varepsilon_{\text{eff}, 0} - 1}\]